I have tried to give a closed form of $\int_{-\infty}^{a} \tan (e^x)dx$ using $\text{Si}(x)$ ( sine integral of x) and $\text{Ci}(x)$ ( cosine integral of $x$) , but I didn't succed really the integral converges for $a <0$ and for $a=0$ has the value $1.1495.. $ as shown here and for $a < 0$ the integral close to $0$ , My question here is : Is this integral has any known closed form ?
Note The titled integral diverges for positive values of $ a$
By setting $x=\log(t)$ we get $$ \int_{-\infty}^{a}\tan(e^x)\,dx = \int_{0}^{e^a}\frac{\tan t}{t}\,dt=\int_{0}^{e^a}\sum_{n\geq 1}\frac{2(4^n-1)\zeta(2n)}{\pi^{2n}} t^{2n-2}\,dt $$ or $$ \sum_{n\geq 1}\frac{2(4^n-1)\zeta(2n)e^{(2n-1)a}}{(2n-1)\pi^{2n}} $$ which is clearly convergent for any $a<\log\frac{\pi}{2}$. Maybe this is known as tangent integral.